Can neural networks be used to find features importance?
This should be possible, considering universal approximation theorem you should be able to build a ann that approximates features that gives the most likely best feature set for a different net to train on. I would us a rnn for with a softmax output layer that ranks features by performance.

You can find a good explanation of softmax here: https://developers.google.com/machine-learning/crash-course/multi-class-neural-networks/softmax
basically it will assign probability values for each output node with all of these values adding up to 1.0